Find the Greatest Common Factor of 40 and 100

Answer:

the Greatest Common Factor of 40 and 100 is 20.

Step-by-step explanation:

Given numbers are 40 and 100.

We will now calculate the prime factors of 40 and 100, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 40 and 100.

How to find the GCF of 40 and 100?

We will first find the prime factorization of 40 and 100. After we will calculate the factors of 40 and 100 and find the biggest common factor number .

Step-1: Prime Factorization of 40

Prime factors of 40 are 2, 5. Prime factorization of 40 in exponential form is:

40 = 23 × 51

Step-2: Prime Factorization of 100

Prime factors of 100 are 2, 5. Prime factorization of 100 in exponential form is:

100 = 22 × 52

Step-3: Factors of 40

List of positive integer factors of 40 that divides 40 without a remainder.

1, 2, 4, 5, 8, 10, 20

Step-4: Factors of 100

List of positive integer factors of 100 that divides 40 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 40 and 100. The biggest common factor number is the GCF number.

So the greatest common factor 40 and 100 is 20.